Cryptogram



. Aug. 14. 1928.

, 1,681,066 w. R. SUMMERS GRYPTOGRAM Filed March 1, 1926 4 Sheets-Sheet 1 THEREFORE WI L'I ALL IF ALL SHALL WORSHIP WORSHIP WIL'I .THOU )ME BE WORSHIP WILT THEREFORE ALL IF THINE SHALL ME BE SHALL IF WORSHIP IF WIL'I IF WILT IF WI LT THEREFORE THOU n ALL IF ME IF IF fl i IF THINE IF THINE SHALL SHALL 3 v I a .r' .5 4 THEREFORE WILT ALL AZL IF SHALL WORSHIP WORSHIP WILT L 6 9 J 1 3 7 I a F THOU/ ME- BE WORSHIP 'WILT THEREFORE ALL IF THINE SHALL "ME BE I SHALL 1F WORSHIP; IF WILT I 7 IF WILT- IF mu 3 THEREFORE THQU 7 IF/ ALL IF- M12 I IF! IF IF! THINEO TF' TmNE IF/ TIIINEO &

SHALL SHALL awuzuto'a MR. Sumneens" as w E A aktoznujl r 1,681,066 w. R. SUMMERS I CRYPTOGRAM Fil March 1926 4 Sheets-Sheet 2 WR. Summezgs 1,681,066 W. R. SUMMERS CRYPTOGRAM F'il March 1, 1926 '4 Sheets-Sheet 4 THEREFORE PUT AWAY F ROM AMONG YOURSELVES THAT WICKED PERSON 1 z a 4 5 6 7 A DOUBLE ms ms UNSTABIE 1s MINDED ALL MAN DOUBLE MANY MAN IN 13 MAN A DOUBLE MAN DOUBLE A mvs ALL DOUBLE MAN DOUBLE MAN 'A MAN DOUBLE A MAN 1 z 9 9 a L 5 3 6 4 A DOUBLE HIS ms UNsrABLE 1s MINDED ALL MAN DOUBLE MAN 7 J 4 z 2 o MAN IN IS mu A DOUBLE MAN DOUBLE A was 5 1 4 Z I 4 .1 1 f ALL DOUBLE MAN DOUBLE MAN A MAN DOUBLE A MAN A DOUBLE MINDED MAN 15 UNSTABLE IN ALL' HIS wAYB 1 z a 4 5 (5 7 6 9 0 avwemtoz wiaammerb merals.

Patented Aug. 14, 1928.

, UNITED STATES WARREN R. SUMMERS, OF SAN DIEGO, CALIFORNIA.

CRYPTOGRAM.

Application filed March 1, 1926. Serial m. 91,654.

This invention relates to cryptography and has as its general object to evolve a c-ryptogram requiring the exercise of the mental faculty of deduction for ts solution.

More specifically, it is an object of the present invention to produce a cryptogram evolved by a system of cipher writing based on mathematical processes, and which cryptogram will be capable of precise solution by mental deduction, without the knowledge or aid of a key, thereby presenting an interest ing problem requiring the exercise of the mental faculties for its solution.

Another object of the invention is to produce a cryptogram capable of prec se solution by mental deduction and which may be published in newspapers, magazines, or periodicals, etc., for solution by the readers thereof, thereby affordingthe readers of the publications an opportunity to exerclse their mental faculties in a pleasurable manner.

In the accompanying drawings:

Figure 1 is a schematic view illustrating a cryptogram developed in accordance with the principles of the invention and as the same would be printed, for solution, 1n amagazme or other publication, or in pamphlet form, and which cryptogram is based on the ar1thmetical process of long division.

Figure 2 is a similar view illustrating the solution of the cryptogram through the deductive translation of words into digit nu- Figure 3 is. a schematic view illustrating the arithmetical process which is 'fOllQWQCllII developing the cryptogram shown in Figure 1. p

Figure 4 is a SClIQlllittlC'VlGW lllustrating the base from which the cryptogram is evolved and the first step inthe evolution thereof. Figure 5 is a view similar to Figure 1, lllustrating a modification of the cryptogram shown in Figure 1, and developed in accordance with the principles of the invention and based on the arithmetical process of long division and in which two selected words I may be employed as a divisor.

Figure 6 is a schematic view illustrating the solution of the cryptogram shown in F igure 5.

Figure 7 is a schematic view similauto Figure 4, illustrating the base from which the cryptogram in Figure 5 is evolved and the first step in the evolution thereof.

Figure 8 is a schematic view illustrating a cryptogram evolved in accordance with the arithmetical process of subtraction and developed in accordance with the principles of the invention.

Figure 9 is a similar view illustrating the solution of the cryptogram shown in Figure 8, through the deductive translation of words into numbers.

Figure 10 is a view similar to Figures 4 and 7, illustrating the base from which the cryptogram shown in Figure 8 is evolved and the first step in the evolution thereof,

Figures 1 to 4 inclusive, illustrate one 'form of cryptogram embodying the invention and the method by which the cryptogram is evolved and likewise the manner in which the same is solved or deciphered, and in this particular instance the evolution and solution of the cryptogram is based on the arithmetical process of long division.

Figure 4 of the drawings illustrates not only the base from which thecryptOgram shown in Figure 1 is evolved, but also illustratesthe result obtained through the deciphering of the cryptogram, and in the said figure there 15 represented a sentence consisting of ten words, although sentences of a fewer number of words may be employed as the base in evolving a cryptogra-m, as for example, as illustrated in Figures 5 and 6 of the drawings and as will presently be more fully explained, and this sentence is taken,

for example, f rom St. Luke, fourth chapter,

seventh verse, and reads: If thou therefore wilt worship me, all shall be thine. The

one evolving the cryptogram assigns toeachword of the sentence a digit nun'ieraland the numerals are assigned in consecutive order so that they will range from 1 to 1 0 or 0, the numeral 1 being assigned to the word If, the numeralQ to the word Thou, etc., the cipher numeral representing 10 being finally assigned to the word Thine.

Figure 3 of the drawings ,illustratesthe mathematical process by which the development of the cryptogram is efi'ectedand the mathematical process in this instance is, as

stated, that of long division. In carrying out this mathematical process, one of the digit numerals assigned to the words of the sentence shown in Figure 4, is selected as a divisor, the numeral 2 being selected in the present instance. The remaining digit numerals are then arranged indiscriminately to form the dividend, the divisor being indicated at A and the dividend at B, and the signs of long division are properlyarranged with respect to the divisor anddividend and with respect to the dividend and quotient which is indicated by the reference character C. As stated, the ren'laining nine digit numerals are arranged indiscriminately in any desired order.

However, as 2 has been selected, in the present instance. as the divisor, the last numeral of the dividend may be t, 6, 8, or the cipher, the dividend, if terminated by any of these nume'als, being exactly divisible by the divisor 2, regardless of the arrangement of the numerals comprising the dividend, as is well recognized. At this point, it may be stated that if the numeral 5 should be selected as the divisor, the remaining nine numerals might be arranged so that the cipher would be the last numeral in the dividend. If 3 should be selected as the divisor, no care need be exercised in the arrangement of the numerals comprising the dividend inasmuch as the sum of the nine digits will in such case, be 42, which is a multiple of 3 and, therefore, any arrangement of the remaining nine numerals would produce a dividend exactly divisible by 3. Therefore, it will be understood that the dividend may comprise an arrangement of the nine numerals divisible exactly by the tenth numeral which is selected as the divisor, or the digit numerals which are to comprise the dividend may be selected without regard to any particular arrangement and without regard to the term of the divisor so that the problem may be such that the last intermediate mathematical process will result in a fraction. Having written the divisor, the dividend, and the signs of division, the mathematical process is carried out as in long division, and in this manner the quotient C is obtained, the various mathematical operations being written down as at D. 'hile ordinz'lrily the example or problem comprising the divisor and dividend would be solved by short division, it is essential, for reasons which will presently be made apparent, that it be solved by long division.

The one evolving the cryptogram, with the solved mathematical problem shown in Figure 3, before him, will translate all of the numerals into the words to which they were originally assigned as in Figure 4, so that the word Thou will appear as the divisor, and the dividend will be represented by the words Me be worship wilt therefore all if thine shall, the sign of division being placed between the words Thou and Me and the quotient readiug'lherefore wilt all if shall worship worship wilt, being placed above the dividend. It will be evident by reference to Figure 1 of the drawings that the intermediate niathennitical operations involved in the solution of the problem shown in Figure 3. and which are indicated in said figure by the reference letter D, will likewise be translated into words. Therefore,

the cryptogram as thus evolved and as shown in the said Figure l, is printed and is in condition to be solved or deciphered.

The cryptogram is dcciphered by the process of mental deduction which invloves a COlIlPttl'lSOll of the words occurring in the devisor, the dividend, the quotient, and the intermediate mathematical operations, a consideration of their location, principally in the portion of the cryptogram representing the intermediate mathematical operations, and a. general deduction of facts from such consideration and comparison. For example, it will be observed that the divisor is the word Thou and in perusing the portion of the cryptogram representing the intermediate mathematical operations it is found that the word Thou occurs as the result of the fifth operation of multiplication of the devisor by a component of the quotient. Therefore, as the result of this operation of multiplication is the divisor itself, the fifth word in the quotient must be the word to which the numeral 1 was originally assigned, for if If times Thou equals 'l hou, then If must be the equivalent of 1. The person solving or deciphering the cryptogram will then write the numeral 1 adjacent the word If at all places where it occurs in the cryptogram as illustrated in Figure 2 of the drawings. Again considering the portion of the eryptogram representing the mathematical operations, it is noted, in the seventh operation of multiplication of the divisor by a component of the quotient. that Thine from If leaves If. 'lherefore, Thine must be the word to which the cipher has been assigned. 'lherefore, the one who is deciphering the cryptogram will write a cipher adjacent the word Thine wherever the same occurs in the cryptograin. It is next to be noted that Thou, the divisor, being multiplied by \Vorship in the quotient, gives a product of 10. namely, If thine, in the seventh and eighth operations of multiplication. and as the only two numerals which multiplied together will give a product of 10, are 5 and 2, then Thou, the divisor, must be the word to which the numeral 2 has been assigned. 'lherefore, the one deciphering the cryptogram will write the numeral 2 in juxtaposition to Thou wherever it occurs in the cryptogram. The word Vol-ship is, therefore, the word to which the numeral 5 has been assigned, and the numeral 5 is written in proximity to the word 'orship wherever it. occurs in the cryptogram. It will he noted that in the third operation, the word Vorship has been brought down from the dividend and that the word Wilt appears below the word \Vorship and that \Vilt subtracted from \Vorship gives If as a remainder. 'lhcrefore. inasmuch as \Vorship is the word to which the numeral 5 has been assigned, the word \Vilt must be the Inn llt)

word to which the numeral 4 has been as signed, and the numeral 4 will, therefore, be written adjacent the word Wilt wherever this word occurs in the cryptogram. It w ll next be observed that inasmuch as filt- 1s the word to which the numeral 4 is assigned, then, in the second operation, Thou mult plied by WVilt or, in other words, 2 multiplied by 4, givesa product of 8, therefore, the word Shall is the word to whlchthe numeral 8 has been assigned. In thlS second operation, it willbe observed that Shall is to be subtracted-from Be and that the result is If which is the word to which the numeral 1 has been assigned, therefore, Be.

must be the word to which the numeral 9 has been assigned. It will next be observed that the divisor Thou to which the numeral 2 has been assigned, multiplied by the first word of the quotient, Therefore, to which the numeral 3 has been assigned, in the first operation of multiplication gives a product of Me and, having previously determined the.

, word to which the numeral 7 has been asi signed,

The numerals associated with the several words having all been determined, it is now a simple matter to write the words in the numerical order of their assigned nu- I merals and the result will be the base shown in Figure 4-, or, in other words, the sentence from which the cryptogram was originally evolved. It would, of course, be obvious that Thou could not be the word to which the digit numeral 5 has been assigned inasmuch as if thiswere the case, there would only be two endings in all of theproducts resulting as a multiplication of the divisor by the words constituting the quotient.

Figures 1 to 4 inclusive, illustrate an embodiment of the invention in which all of the digit numerals are employed, namely, the numerals ranging from 1 to the cipher. Figures 5 to 7 inclusive illustrate an em bodiment of the invention in which less than the total number of digit numerals are employedand in which cryptograms may be evolved from a sentence consisting, for example, of six, seven, eight or nine words. Likewise, in the embodiment shown in Figures 1 to 4 inclusive, a single one of the words is selected as the divisor,fbut as will now be explained, in the embodiment shown in Figures 5, 6 and 7, at least two words may be selected as the divisor. As shown in Figure 7 ofthe drawings, the sentence, or, in other words, the base from which the crypt-ogram is evolved, reads: Therefore put away divisor and dividend will then be arranged in their proper order and the process of long division carried out in substantially the manner shown in Figure 3 of the drawings, and after the mathematical problem has been solved, the numerals are translated into words so as to produce the cryptogram shown in Figure 5 of the drawings. It will be observed that the first word of the quotient is Therefore and that in the first operation of multiplication this word times, the

words Put put gives the result Put put which is the divisor itself, and consequently Therefore must be the first word of the sentence and the. numeral lis, therefore, written, as shown in F igure6, adjacent the word Therefore wherever. it occurs throughout the eryptogram. It will be observed that the last word in the quotient is the same as each of the two wordsgin the divisor or, in other words, the word Put and for this reason it is evident that this word cannot represent the digit numeral 1 for if it did the result of the operation of multiplication would be Put put. By the process of mental deduction we know that the word Put cannot represent so large a number or digit numeral as 3 for ifit did the product. would be 99 or, in other words, the largest number which can be represented by two digit numerals and since there is a remainder as a result of the last mathematical process in the problem, Put must represent the digit numeral 2. As Put represents 2, and as Put put, which is thedivisor, multiplied by Put put, in the last process of multiplication of the divisor by the last wordof the quotient is From from, we therefore understand that From from represents 44 and, therefore, From equals 4. It will be observed that From from subtracted from From yourselves gives a remainder of PM and since we have determined that Put represents the digit numeral 2 and. From represents the digit numeral 4, then it is deduced that Yourselves must be the word to which the digit numeral 6 has been assigned. It is next noted that in the fourth process of sub traction there is no remainder when Yourselves is subtracted from That and since it is obvious that these two words represent or have been assigned different digit numerals, it is evident that 1 was borrowed from the digit numeral assigned to the word That in the performance of the operation of subtraction and consequently the word That is lin ill)

the word to which the digit numeral 7 has been assigned. Having ascertained that the word Put is the word to which the digit numoral 2 has been assigned and the word From is the word to which the digit numeral 4 has been assigned, and observing that, in the third process of multiplication of the divisor by the corresponding word of the quotient, the resultis lVicltcd wicked, then \Viched wicked must represent 88 and consequently the word lVickcd is the word to which the digit numeral 8 has been assigned. It is next observed that in subtracting icked wicked from Person among, there is no remainder in the left hand column or, in other words, no remainder as the result of subtraction of icked from Person, and since the two words lVicked and Person are words to which two dili'erent digit numerals have been assigned, it is evident that 1 was borrowed from the digit numeral to which the word Person was assigned, and it is also obvious that the numeral to which the word Person has been assigned must be higher in value by 1 than the numeral to which the word lViclted has been assigned, since there is no remainder. Consequently, since icked is the word to which the digit numeral Shas been assigned, the digit numeral to which the word Person has been assigned must be 9. In the third. process of subtraction, it is noted that icked from Among leaves a remainder of That and since it is evident that 1 was borrowed from 9, being the digit numeral assigned to Person, then, since we have determined that That is the word to which the digit numeral 7 has been assigned and the word Yourselves is the word to which the digit numeral 6 has been assigned, the words Person among must represent 15 and consequently Among must be the word to which the digit numeral 5 has been assigned. It is found that the fourth word in the quotient is Away and since it is found that the product of Away times Put put equals Yourselvcs yourselves, then the word Away must he the word to which the numeral 3 has been assigned.

lt will be observed that in the embodin'ient of the invention inst described, the dividend is not evactly divisible by the divisor and that less than the total number of digit numerals are employed. and in these respects this embodiment differs from the embodiment shown in Figures 1 to 4: inclusive.

Figures 8, 9 and 10 of the drawings illustrate the evolution and solution of a cryptogram From a base sentence and based on the aritlnnetical )roccss of subtraction, and as shown in Figure 10 of the drawings, the sentence or base from which the cryptogram is evolved and which likewise constitutes the solution of the cryptogram, reads: A double minded man is unstable in all his ways, and

to the words of this sentence are assigned in consecutive order, the digit numerals 1 to 0 inclusive. In evolving the cryptograni, which is shown in Figure 8, from the base shown in Figure 10, the digit numerals are selected and arranged to constitute a minuend and the said numerals are likewise selected and arranged to constitute the subtrahcnd, and the arithmetical process of :aihtraction is carried out and in this manner the ren'lainder is obtained. The one evolving the cryptogram will then translate the digit numerals into their respective words and the result will be the cryptogram shown in the said Figure 8. Figure 9 represents the manner in which the cryptogram is solved by deduction. i

In solving the cryptogram shown in Figure 8 ol' the drawings, it will be observed that Man is subtracted l' om the words A double and it is evident therefore that Man could not be subtracted from Double alone in this process 01 solution ol the problem. 'lhereforc, 1 must be borrowed from the word A and we know that A, must be the word to which the digit numeral 1 has been assigned for otherwise there would be two words as the remainder. It is next noted that A, being the word to which the digit numeral 1 has been assigned, subtracted from Double, in the ninth process of suliitraction, givis a ltil'lilllltlQl' of A, then Double must be the word to which the digit numeral 2 has been assigned. Since in the eighth process of subtraction Double, which is the word to which the digit numeral :2 has been assigned, subtracted i'rorn Man, gives a remainder of Double, then Man must the word to which the digit numeral 4: has been assigned. Likewise, sincc in'the last process of subtraction lVays subtracted from Man, which latter word is that-to which the digit numeral 4 has been assigned, gives the remainder of Man, then \Vays must be the word to which the digit numeral 0 or cipher has been assigned. In the first process of subtlnction. and having ascertained that A double equals 12, then Man which is the word to which the digit numeral-1 has been assigned, subtracted from 1'2 giving a remainder of All, All must be the word to which the digit numeral 8 has been assigned. Since as a result of the sixth process ot subtraction, Double from Minded gives a remainder of A and Double and A are respectively the words to which the digit numerals 2 and 1 have been assigned, then Minded must be the word to which the digit numeral 3 has been assigned. Since A is the word to which the digit numeral 1 has been assigned and Man is the word to which the digit numeral -Lt has been assigned, it will be evident from the fifth process of subtraction-that A from Is, giving a remainder of Man, Is must he the word to which the llfi digit numeral 5 has been assigned. and referring to the third process of subtraction in which Is is subtracted from His, giving a remainder of Man, it is evident that Is is the word to which the digit numeral 9 has been assigned. Observing the second process of subtraction, in which In is subtracted from Is, and having ascertained that His and Double are respectively the words to which the digit numerals E) and 2 have been assigned, then In must be the word to which the digit numeral 7 has been assigned. Likewise, having ascertained that Man and Double are respectively the words to which the digit nu merals 4 and 2 have been assigned and observing from the fourth process of substraction that Man or 4 from Unstable gives a remainder of Double or 2. then Unstable must be the word to which the digit numeral (3 has been assigned. Vriting the words in their numerical order, the base sentence shown in Figure 10 is obtained and the cryptogram has thus been deciphered.

In the illustrated and described embodiments of the invention, the cryptograms are based on the arithmetical processes of long division and subtraction, but the invention is not restricted to these mathematical processes as cryptograms may be evolved based on the arithmetical processesof the extraction of square and cube roots, on problems involving partial payments, percentage, complex fractions, or, in fact, any arithmetical process.

I have previously referred to the sentence from which the cryptogram is evolved, as a base and have appropriated this term to a CH mean a sentence, a clause, a phrase or any intelligently arranged group of words, and while no cryptogram evolved in accordance with the present invention can have as its base more than ten words, it will be evident that a number of sentences, or, in fact, an unlimited amount of text matter, might be represented in cipher form by selecting successive groups of ten words each.

It will be evident from the foregoing, that the cryptogram is capable of solution without the employment of a key and that in this respect, the cryptogram is distinct in its character from the ordinary cryptograms which are of such a nature as to require the knowledge of a key for their solution.

It will be evident that in certain arithmetical problems there are initially present numerical t'erms whioh may be considered as the fundamental components of the prob lem to be solved and that there are intermediate components representing the arithmetical processes by which the result or what might be termed the resultant component of the problem is obtained, in accordance with the character of the particular arithmetical problem. Thus, for example, in the arithmetical process of long division, the divisor and dividend constitute the fundamental components of the problem to be solved and the quotient constitutes the resultant component of the problem, the arithmetical processes resulting from the multiplication of the divisor by a numeral of the quotient and the subtraction of the product from the result of the preceding operation, all. constituting the intermediate components of the solved problem and inasmuch as ever arithmetical process must involve at least two fundamental components and a resultant component or two fundamental components, intermediate components, and a resultant component, these terms will be employed in the claims in view of the fact that the invention is not limited to any particular arithmetical or mathematical process.

It will be evident that by the publication of cryptograms or cipher quotations in accordance with the principles of the present invention, in newspapers and periodicals, quotations which are instructive and inspiring may be impressed upon the mind.

Having thus described the invention, what I claim is:

1. A sheet bearing a cryptogram comprising words arranged and grouped in accordance with a solved problem in mathematics in which the numerals constituting the fundamental and resultant components of the solved problem are selected digit numerals assigned consecutively to a series of words constituting a base.

2. A sheet bearing a cryptogram comprising words arranged and grouped in accord ance with a solved problem in mathematics, in which problem the numerals constituting the fundamental, intermediate and resultant components of the solved problem are selected digit numerals assigned consecutively to a series of words constituting a base.

3. A sheet bearing a cryptrogram comprising words ar 'anged and grouped in accordance with a solved problem in long division in which the numerals constituting the divisor and the dividend, areselected digit numerals assigned consecutively to a series of words constituting a base and in which the arithmetical operations incident to the solution of the problem are likewise represented by numerals assigned to the words constituting the base.

In testimony whereof I afiix my signature.

WARREN R. SUMMERS. [L. 8.]

Ill) 

